A Fuzzy Plug-and-Play Neural Network-Based Convex Shape Image Segmentation Method
Abstract
:1. Introduction
2. Related Work
2.1. The BLF-Based Convex Shape Image Segmentation Model
2.2. A P&P–ADMM Image Segmentation Framework with a DCNN Denoiser
3. Our Proposed Convex Shape Image Segmentation Method
3.1. Our Proposed Model
3.2. Algorithm to Our Model
Algorithm 1 Our proposed plug-and-play neural network-based convex shape image segmentation algorithm (the PPA–CS algorithm). |
Initialization: initialize manually, and , give some parameters, including , , , , and , and set the iteration index . |
Repeat: |
update in (18); |
update in (18); |
update in (18); |
project ; |
; |
Until a stopping criterion is satisfied |
Output: our final estimated FMF result . |
4. Numerical Results and Discussion
4.1. Environmental Setting
4.2. Segmentation Results on BSDS500 and WSED
4.3. Model Sensitivity to Initial Contours
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
SDF | Signed distance function |
BLF | Binary label function |
FMF | Fuzzy membership function |
TV | Total variation |
DCNNs | Deep convolutional neural networks |
P&P | Plug-and-play |
ADMM | Alternating direction method of multipliers |
HQS | Half-quadratic splitting |
RE | Relative error |
BSDS500 | The Berkeley segmentation dataset and benchmark 500 |
WSED | The Weizmann segmentation evaluation database |
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(1, 1) | (1, 2) | (1, 3) | (1, 4) | (1, 5) | (2, 1) | (2, 2) | (2, 3) | (2, 4) | (2, 5) | |
---|---|---|---|---|---|---|---|---|---|---|
BLF-TV-CS | F | T | F | F | T | F | F | F | T | T |
PPA-CS | T | T | T | T | T | T | T | T | T | T |
(1, 1) | (1, 2) | (1, 3) | (1, 4) | (1, 5) | (2, 1) | (2, 2) | (2, 3) | (2, 4) | (2, 5) | |
---|---|---|---|---|---|---|---|---|---|---|
BLF-TV-CS | F | T | F | T | F | F | F | T | T | F |
PPA-CS | T | T | T | T | T | T | T | T | T | T |
(1, 1) | (1, 2) | (1, 3) | (1, 4) | (1, 5) | (2, 1) | (2, 2) | (2, 3) | (2, 4) | (2, 5) | |
---|---|---|---|---|---|---|---|---|---|---|
Figure 2 | ||||||||||
Figure 3 |
Methods | ||||||||
---|---|---|---|---|---|---|---|---|
Iters | Time/s | Iters | Time/s | Iters | Time/s | Iters | Time/s | |
BLF-TV-CS | 94 | 7.74 | 65 | 5.39 | 19 | 1.96 | 97 | 8.37 |
PPA-CS | 18 | 7.95 | 28 | 12.87 | 18 | 7.95 | 64 | 31.22 |
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Zhang, X.; Han, Y.; Lin, S.; Xu, C. A Fuzzy Plug-and-Play Neural Network-Based Convex Shape Image Segmentation Method. Mathematics 2023, 11, 1101. https://doi.org/10.3390/math11051101
Zhang X, Han Y, Lin S, Xu C. A Fuzzy Plug-and-Play Neural Network-Based Convex Shape Image Segmentation Method. Mathematics. 2023; 11(5):1101. https://doi.org/10.3390/math11051101
Chicago/Turabian StyleZhang, Xuyuan, Yu Han, Sien Lin, and Chen Xu. 2023. "A Fuzzy Plug-and-Play Neural Network-Based Convex Shape Image Segmentation Method" Mathematics 11, no. 5: 1101. https://doi.org/10.3390/math11051101
APA StyleZhang, X., Han, Y., Lin, S., & Xu, C. (2023). A Fuzzy Plug-and-Play Neural Network-Based Convex Shape Image Segmentation Method. Mathematics, 11(5), 1101. https://doi.org/10.3390/math11051101